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2 Answers
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EdX will release its learning platform as open-source software so that
anyone around the world can adopt and improve this shared tool. Timing
of the release has not yet been determined.

And more recently in an article (Sept 2012) about MongoDB getting involved:

The eventual goal of the collaboration is to both provide all of
10gen's training for free online and to release the entire EdX
platform under an open-source license.

The edX homepage still lists jobs for platform developers, so looks like it is still a work in progress. In the meantime Google has released an experimental Course Builder platform, or there is the popular Moodle.